Maximising Profits for Broadway Theatres

team
Felix, Jeni, Janet

University of Edinburgh

2021-12-01

Dataset

  • Tidy Tuesday project file
  • Compiled from Playbill, a magazine for theatres
  • Information on weekly grosses, average ticket price, etc of different theatre shows
  • 14 variables, 47,524 observations
  • weekly_gross, avg_ticket_price, seats_in_theatre, weeks_running

Dataset

## Rows: 47,524
## Columns: 14
## $ week_ending          <date> 1985-06-09, 1985-06-09, 1985-06-09, 1985-06-09, …
## $ week_number          <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1…
## $ weekly_gross_overall <dbl> 3915937, 3915937, 3915937, 3915937, 3915937, 3915…
## $ show                 <chr> "42nd Street", "A Chorus Line", "Aren't We All?",…
## $ theatre              <chr> "St. James Theatre", "Sam S. Shubert Theatre", "B…
## $ weekly_gross         <dbl> 282368, 222584, 249272, 95688, 61059, 255386, 306…
## $ potential_gross      <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
## $ avg_ticket_price     <dbl> 30.42, 27.25, 33.75, 20.87, 20.78, 31.96, 28.33, …
## $ top_ticket_price     <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, N…
## $ seats_sold           <dbl> 9281, 8167, 7386, 4586, 2938, 7992, 10831, 5672, …
## $ seats_in_theatre     <dbl> 1655, 1472, 1088, 682, 684, 1018, 1336, 1368, 148…
## $ pct_capacity         <dbl> 0.7010, 0.6935, 0.8486, 0.8405, 0.5369, 0.9813, 1…
## $ performances         <dbl> 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 0, 8, 8…
## $ previews             <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0…

Research Question

  1. What are the factors that can affect the average ticket price of a show?
  2. Hence, how does average ticket price then influence the weekly gross revenue earned?

Gross Weekly Revenue

MUTATE Theatre Size

less than 750 seats = small, 750 ~ 1300 = medium, more than 1300 = large

Gross Weekly Revenue

Percentage Capacity

Week Running

Number of Performances Per Week

Main Research

Average Ticket Price vs Seats Sold

The Log Model

Set Model

logxy_preliminary <-
  linear_reg() %>%
  set_engine("lm")

logxy <- logxy_preliminary %>%
  fit(gross_log ~ price_log, data = grosses_log)

\[y=e^{6.81}x^{1.51}\]

R Squared and RMSE

## # A tibble: 1 × 3
##   .metric .estimator .estimate
##   <chr>   <chr>          <dbl>
## 1 rsq     standard       0.913
## # A tibble: 1 × 3
##   .metric .estimator .estimate
##   <chr>   <chr>          <dbl>
## 1 rmse    standard       0.445
## # A tibble: 1 × 3
##   .metric .estimator .estimate
##   <chr>   <chr>          <dbl>
## 1 rsq     standard       0.910
## # A tibble: 1 × 3
##   .metric .estimator .estimate
##   <chr>   <chr>          <dbl>
## 1 rmse    standard       0.451

RSQ-RMSE Table & Cross Validation

Pred RSQ RMSE
Test Data 0.910 0.451
Train Data 0.913 0.445 
## # A tibble: 2 × 6
##   .metric .estimator  mean     n std_err .config             
##   <chr>   <chr>      <dbl> <int>   <dbl> <chr>               
## 1 rmse    standard   0.445     5 0.00415 Preprocessor1_Model1
## 2 rsq     standard   0.912     5 0.00569 Preprocessor1_Model1
##       id              .metric           .estimator          .estimate     
##  Length:10          Length:10          Length:10          Min.   :0.4346  
##  Class :character   Class :character   Class :character   1st Qu.:0.4436  
##  Mode  :character   Mode  :character   Mode  :character   Median :0.6760  
##                                                           Mean   :0.6784  
##                                                           3rd Qu.:0.9135  
##                                                           Max.   :0.9241  
##    .config         
##  Length:10         
##  Class :character  
##  Mode  :character  
##                    
##                    
##

Equation & Graph

\[y=e^{6.81}x^{1.51}\]

Conclusion

  • theatre size, percentage capacity, average price influenced weekly gross
  • number of performances per week, total number of weeks show ran for did not
  • modelled relationship between average ticket price and weekly gross revenue, which was found to be positive

Limitations & Extensions

  • Limitations: might only be a particular set of customers in Broadway, larger samples of data

  • Future Extension: model that can include the exponential curvature of the graph

Thank you for watching